Finite Group Databasebeta

← C2×#13069013 #14755330

Subgroups — C2×#13069013 #14755330

Order 2816.

2526 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66927C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C22×#66887C211yesmaximal, characteristic, complemented
6#13069013C218yesmaximal, direct product factor
7C2×#10622161C211yesmaximal, characteristic, complemented
8C2×C11×#339C211yesmaximal, characteristic, complemented
9C23×D44—22no—
10C23×D44C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623052—22no—
18#10623052—22no—
19#10623052—22no—
20#10623052C2214yescomplemented
21C2×#66946—22no—
22C2×C22⋊C4×D11—22no—
23C2×#66927—22no—
24C2×#66927—24no—
25C2×#66927C418yescomplemented
26C2×#66927C2214yes—
27C2×C4×D44—22no—
28#10622744—22no—
29#10622744C2214yescomplemented
30C2×#66887—24no—
31C2×#66887C2214yescomplemented
32C2×#66885—22no—
33#10622614—22no—
34#10622614C2214yescomplemented
35C2×#66873—22no—
36C11×#339C2214yescomplemented
37#10622161C2214yescomplemented
38C24×D11—21no—
39C24×D11D412yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×D44—21no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44—21no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—216no—
55C22×D44—28no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—416no—
59C22×D44C2×C414yes—
60C22×D44C2×C414yescomplemented
61C22×D44D412yes—
62C22×D44D414yes—
63C22×D44C2312yes—
64C22×D44C2312yes—
65C22×C4×D11—24no—
66C2×C11×M16—21no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2312yes—
70C22×C8×C11—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117D412yescomplemented
74C11×#117C2312yes—
75C2×C11×C4⋊C4D412yescomplemented
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—22no—
80C2×C42×C11C2×C414yescomplemented
81C2×C42×C11C2312yes—
82C2×C22⋊Dic11—21no—
83C2×(C2×D11)⋊C4—24no—
84#66979—21no—
85#66979—21no—
86#66979D412yescomplemented
87#66979C2312yes—
88C2×C4⋊Dic11D412yescomplemented
89C2×C4×Dic11—21no—
90C2×#4318—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2312yes—
94C22×C11⋊C8—21no—
95#66946—28no—
96#66946—28no—
97C22⋊C4×D11—28no—
98C22⋊C4×D11—28no—
99#66927—216no—
100#66927—28no—
101#66927C2×C4116yescomplemented
102C4×D44—28no—
103C4×D44—28no—
104#66887—28no—
105#66885—28no—
106#66873—28no—
107C2×#1887—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—22no—
114C23×D11—48no—
115C23×D11—48no—
116C23×D11—41no—
117C23×D11—41no—
118C23×D11—42no—
119C23×D11C22⋊C418yes—
120C23×D11C2×D414yes—
121C22×C4×C11—28no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—22no—
136C2×D44—232no—
137C2×D44—24no—
138C2×D44—24no—
139C2×D44—24no—
140C2×D44—24no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—24no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—24no—
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—24no—
152C2×D44—24no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44—464no—
163C2×D44—432no—
164C2×D44—41no—
165C2×D44—41no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44C22⋊C418yes—
172C2×D44C22×C414yes—
173C2×D44C22×C414yescomplemented
174C2×D44C2×D414yes—
175C2×C4×D11—216no—
176C2×C4×D11—88no—
177C11×M16—22no—
178C11×M16—22no—
179C11×M16—42no—
180C2×C8×C11—22no—
181C2×C8×C11—42no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4C2×D414yescomplemented
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C42×C11—24no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11C22×C414yescomplemented
191C22⋊Dic11—22no—
192C22⋊Dic11—22no—
193(C2×D11)⋊C4—216no—
194C4⋊Dic11—22no—
195C4⋊Dic11C2×D414yescomplemented
196C4×Dic11—22no—
197C4×Dic11—22no—
198#4318—22no—
199#4318—22no—
200#4318—42no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—42no—
203C22×#127—111no—
204C2×#518—111no—
205C2×#418—111no—
206C2×#418—111no—
207C22×#100—111no—
208#1887—118no—
209C2×#339—111no—
210C2×#339D1111yescharacteristic, complemented
211C23×C11—24no—
212C23×C11C2×C22⋊C412yes—
213C23×C11#12011yescharacteristic
214C23×C11#12011yescharacteristic
215C23×C11#12312yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—28no—
219C22×D11—24no—
220C22×D11—28no—
221C22×D11—24no—
222C22×D11—48no—
223C22×D11—416no—
224C22×D11—48no—
225C22×D11—416no—
226C22×D11—48no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—88no—
232C22×D11—84no—
233C22×D11—88no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11C2×C22⋊C418yes—
237C2×C4×C11—216no—
238C2×C4×C11—28no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—44no—
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C4×D412yes—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C4×D412yes—
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12112yes—
250C2×C4×C11#12112yes—
251C2×C4×C11#12112yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#12312yes—
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—24no—
261C2×Dic11—44no—
262D44—24no—
263D44—24no—
264D44—24no—
265D44—24no—
266D44—24no—
267D44—24no—
268D44—28no—
269D44—28no—
270D44—464no—
271D44—42no—
272D44—42no—
273D44—44no—
274D44—44no—
275C4×D11—816no—
276C8×C11—42no—
277C11⋊C8—42no—
278C23×D4—111no—
279C23×D4—111no—
280C23×D4—222no—
281C22×M16—111no—
282C22×M16C2×D1111yescharacteristic
283C2×#127—114no—
284C2×#127—118no—
285C2×#127—222no—
286C2×#127—224no—
287#518—114no—
288#518—222no—
289#518—222no—
290#518—222no—
291C2×C4×D4—222no—
292C2×C4×D4—222no—
293C2×#117—111no—
294C2×#117C2×D1111yescharacteristic
295C22×C22⋊C4—222no—
296C22×C42C2×D1111yescharacteristic
297#418—114no—
298#418—114no—
299#418—222no—
300#418—222no—
301C2×#102—222no—
302C2×#102—222no—
303C2×#100—114no—
304C2×#100—224no—
305#339—114no—
306#339C2×D1114yescomplemented
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—22no—
310C22×C11—22no—
311C22×C11#38612yes—
312C22×C11#38612yes—
313C22×C11#45314yes—
314C22×C11C22×C22⋊C411yescharacteristic
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12311yescharacteristic
317C2×D11—28no—
318C2×D11—416no—
319C2×D11—48no—
320C2×D11—48no—
321C2×D11—48no—
322C2×D11—44no—
323C2×D11—84no—
324C2×D11—88no—
325C2×D11—84no—
326C2×D11—88no—
327C2×D11—88no—
328C2×D11—84no—
329C4×C11—28no—
330C4×C11—44no—
331C4×C11#38612yes—
332C4×C11#38612yes—
333C4×C11C2×C4×D411yescharacteristic
334C4×C11C2×C4×D411yescharacteristic
335C4×C11C2×#12111yescharacteristic
336C4×C11C2×#12111yescharacteristic
337Dic11—44no—
338C25—112no—
339C25—221no—
340C22×D4—114no—
341C22×D4—114no—
342C22×D4—112no—
343C22×D4—114no—
344C22×D4—112no—
345C22×D4—112no—
346C22×D4—2216no—
347C22×D4—228no—
348C22×D4—221no—
349C22×D4—221no—
350C22×D4—221no—
351C22×D4—221no—
352C22×D4—222no—
353C22×D4—222no—
354C22×D4—221no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4—221no—
358C22×D4—221no—
359C22×D4—222no—
360C22×D4—222no—
361C22×D4—222no—
362C22×D4—4416no—
363C23×C4—21no—
364C23×C4—224no—
365C23×C4C22×D1111yescharacteristic
366C2×M16—21no—
367C2×M16—22no—
368C2×M16—22no—
369C2×M16—112no—
370C2×M16—221no—
371C2×M16—222no—
372C2×M16—222no—
373C2×M16C22×D1112yes—
374C22×C8—21no—
375C22×C8—221no—
376#127—1116no—
377#127—2216no—
378#127—228no—
379C4×D4—228no—
380C4×D4—228no—
381C4×D4—228no—
382C4×D4—228no—
383#117—21no—
384#117—21no—
385#117—112no—
386#117—112no—
387#117—221no—
388#117—221no—
389#117D4412yescomplemented
390#117C22×D1112yes—
391C2×C4⋊C4—112no—
392C2×C4⋊C4D4412yescomplemented
393C2×C22⋊C4—21no—
394C2×C22⋊C4—228no—
395C2×C22⋊C4—228no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—221no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—221no—
402C2×C42C4×D1114yescomplemented
403C2×C42C22×D1112yes—
404#102—228no—
405#102—228no—
406#100—228no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—22no—
410C2×C11#188714yescomplemented
411C2×C11C2×#38611yescharacteristic
412C2×C11C2×#45312yes—
413D11—48no—
414D11—84no—
415C24—118no—
416C24—114no—
417C24—222no—
418C24—222no—
419C24—224no—
420C24—224no—
421C24—222no—
422C24—448no—
423C24—448no—
424C24—441no—
425C24—441no—
426C24—442no—
427C24D4×D1111yescharacteristic
428C2×D4—118no—
429C2×D4—114no—
430C2×D4—114no—
431C2×D4—114no—
432C2×D4—2232no—
433C2×D4—224no—
434C2×D4—224no—
435C2×D4—224no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—222no—
439C2×D4—222no—
440C2×D4—224no—
441C2×D4—224no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—224no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—4432no—
459C2×D4—4464no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—442no—
465C2×D4—442no—
466C2×D4—442no—
467C22×C4—28no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—2216no—
472C22×C4—222no—
473C22×C4—888no—
474C22×C4C2×C4×D1112yes—
475C22×C4C2×D4411yescharacteristic
476C22×C4C2×D4411yescharacteristic
477C22×C4#433912yes—
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1112yes—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4#434312yes—
483C22×C4C23×D1111yescharacteristic
484M16—22no—
485M16—22no—
486M16—42no—
487M16—222no—
488M16—222no—
489M16—442no—
490C2×C8—22no—
491C2×C8—42no—
492C2×C8—222no—
493C2×C8—442no—
494C4⋊C4—22no—
495C4⋊C4—114no—
496C4⋊C4—222no—
497C4⋊C4C2×D4414yescomplemented
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—2216no—
501C22⋊C4—222no—
502C22⋊C4—222no—
503C42—24no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—222no—
508C42—222no—
509C42C2×C4×D1114yescomplemented
510C11C2×#188711yescharacteristic, complemented, Sylow
511C23—24no—
512C23—118no—
513C23—224no—
514C23—228no—
515C23—224no—
516C23—228no—
517C23—224no—
518C23—448no—
519C23—4416no—
520C23—448no—
521C23—4416no—
522C23—448no—
523C23—442no—
524C23—442no—
525C23—444no—
526C23—444no—
527C23—884no—
528C23—888no—
529C23—884no—
530C23—888no—
531C23—884no—
532C23C22⋊C4×D1112yes—
533C23#6693511yescharacteristic
534C23#6693511yescharacteristic
535C23#6694712yes—
536C23C2×D4×D1111yescharacteristic
537D4—224no—
538D4—224no—
539D4—224no—
540D4—224no—
541D4—224no—
542D4—224no—
543D4—228no—
544D4—228no—
545D4—4464no—
546D4—442no—
547D4—442no—
548D4—444no—
549D4—444no—
550C2×C4—28no—
551C2×C4—216no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—44no—
555C2×C4—224no—
556C2×C4—444no—
557C2×C4—8816no—
558C2×C4C4×D4412yes—
559C2×C4C4×D4412yes—
560C2×C4C22⋊C4×D1112yes—
561C2×C4#6693511yescharacteristic
562C2×C4#6693511yescharacteristic
563C2×C4#6693712yes—
564C2×C4#6693712yes—
565C2×C4#6694612yes—
566C2×C4#6694612yes—
567C2×C4#6694712yes—
568C2×C4#6694812yes—
569C2×C4#6694812yes—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4C22×D4411yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×D4×D1111yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C8—42no—
577C8—442no—
578C22—22no—
579C22—22no—
580C22—24no—
581C22—24no—
582C22—228no—
583C22—448no—
584C22—448no—
585C22—448no—
586C22—4416no—
587C22—444no—
588C22—884no—
589C22—888no—
590C22—884no—
591C22—888no—
592C22—884no—
593C22—888no—
594C22#1062227812yes—
595C22#1062227812yes—
596C22#1062243514yes—
597C22C2×C22⋊C4×D1111yescharacteristic
598C22C2×#6693511yescharacteristic
599C22C2×#6694711yescharacteristic
600C4—28no—
601C4—44no—
602C4—444no—
603C4#1062227812yes—
604C4#1062227812yes—
605C4C2×C4×D4411yescharacteristic
606C4C2×#6693711yescharacteristic
607C4C2×#6694611yescharacteristic
608C4C2×#6694811yescharacteristic
609C2—21no—
610C2—21no—
611C2—22no—
612C2—448no—
613C2—884no—
614C2#1306901314yesdirect product factor
615C2C2×#1062227811yescharacteristic
616C2C2×#1062243512yes—
subgroupG/H
centerC23#66935
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC23×C11#120
prime radicalC22×#66927C2
cosocleC22×C4×C11C24
hypercenterC2×#339D11
hypocenterC11C2×#1887
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10622744C2semidirect
4. C2×#10622614C2semidirect
5. C22×#66887C2semidirect
6. #13069013C2direct (N × H)
7. C2×#10622161C2semidirect
8. C2×C11×#339C2semidirect
20. #10623052C22semidirect
25. C2×#66927C4semidirect
29. #10622744C22semidirect
31. C2×#66887C22semidirect
34. #10622614C22semidirect
36. C11×#339C22semidirect
37. #10622161C22semidirect
60. C22×D44C2×C4semidirect
73. C11×#117D4semidirect
75. C2×C11×C4⋊C4D4semidirect
80. C2×C42×C11C2×C4semidirect
86. #66979D4semidirect
88. C2×C4⋊Dic11D4semidirect
101. #66927C2×C4semidirect
173. C2×D44C22×C4semidirect
183. C11×C4⋊C4C2×D4semidirect
190. C42×C11C22×C4semidirect
195. C4⋊Dic11C2×D4semidirect
210. C2×#339D11semidirect
306. #339C2×D11semidirect
389. #117D44semidirect
392. C2×C4⋊C4D44semidirect
402. C2×C42C4×D11semidirect
410. C2×C11#1887semidirect
497. C4⋊C4C2×D44semidirect
509. C42C2×C4×D11semidirect
510. C11C2×#1887semidirect
614. C2#13069013direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669272
C2×#106230522
C2×#106227442
C2×#106226142
C22×#668872
#130690132
C2×#106221612
C2×C11×#3392
C2×#188711